Question

Two of the most expensive cars in the world are car A and car B. The prices of these two cars differ by more than ​$. The price of car A is ​$.
a. Assuming that you do not know which model is more​ expensive, write an absolute value inequality that describes this situation. Use x for the price of car B.
b. What are the possibilities for the price of car​ B?

Answer 1

Answer:

Part a:

Price of car A = $131,745    and price of car B is unknown = x

There are two possible cases: 1) Car A is the more expensive car, and 2) car B is the more expensive one. We start by analyzing both cases separately:

Case 1) If car A is the more expensive car, we could write the difference in prices in mathematical form, using the "larger than" symbol: ">"

$131,745 - x > $15,000 that reads :"the price of car A ($131,745) minus the price of car B (x) is MORE THAN (>) $15,000

Case 2) Car B is more expensive than A, so we can write:

x - $131,745 > $15,000 that reads: "the price of car B (x) minus the price of car A ($131,745) is MORE THAN (>) $15,000

Both inequalities that we wrote above can be condense in a single inequality if we use the "absolute value" mathematical symbol thus expressing that the difference between both prices in absolute value must be larger than $15,000:

| $131,745 - x | > $15,000

Part b) We can solve for x in the first inequality we wrote:

$131,745 - $15,000 > x therefore x < $116,745

and also we can solve for x in the second inequality given us the second possibility:

x - $131,745 > $15,000  therefore x > $146,745